@article{1194.46014,
author="Alspach, Dale E.",
title="{Good $\ell_2$-subspaces of $L_p$, $p>2$.}",
language="English",
journal="Banach J. Math. Anal. ",
volume="3",
number="2",
pages="49-54",
year="2009",
abstract="{In a recent preprint, {\it R.\,Haydon, E.\,Odell}\/ and {\it
    Th.\,Schlumprecht} [``Small subspaces of $L_p$,'' \url{arXiv:0711.3919}]
    show that a Hilbertian subspace of $L_p$, $p>2$, contains a further subspace
    $Z$ that is $(1+\varepsilon)$-isomorphic to $\ell_2$ and complemented in
    $L_p$ by a projection of norm $\le (1+\varepsilon)\gamma_p$, where
    $\gamma_p$ is the $L_p$-norm of a standard Gaussian random variable. Their
    proof uses random measures and types \`a la Krivine and Maurey. Here, the
    author gives another proof that avoids these means and depends only on a
    version of the central limit theorem for martingales.}",
reviewer="{Dirk Werner (Berlin)}",
keywords="{subspaces of $L_p$; well complemented subspace; Hilbertian subspace;
    central limit theorem}",
classmath="{*46B09 (Probabilistic methods in Banach space theory)
46B25 (Classical Banach spaces in the general theory of normed spaces)
46E30 (Spaces of measurable functions)
}",
}